Some games, like tennis or ping pong, reach a state called deuce. this means that the score is tied and a player wins the game when they get two points ahead of the other player. suppose the probability that you win a point is p and this is true independently for all points. if the game is at deuce what is the probability you win the game?

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb